
Obviously it admits a solution\((\frac{\delta }{c_4}(1-e^{-c_4(N-t)}),0)\) . Then from the maximal solution argument (Theorem 2.3 of [1]}), we know that the solution \((\underline{P}(i), \underline{\Lambda }(i))\)  of (REF ) satisfies
\(\underline{P}(t, i)\ge \frac{\delta }{c_4}(1-e^{-c_4(N-t)}).\) 
